Many scientific, medical, or other still images and image sequences are conveyed from an image sensor via a signal that contains additive noise that contaminates the signal. The noise takes the form of a random variable, typically approximately normally distributed, that is sampled independently at different locations in the image. These locations can vary in size from single pixels to resolution elements. The noise distribution can be independent of the image value (“pure additive noise”) or dependent on the image value (“variable additive noise”).
An example of pure additive noise is read noise of a digital image detector. Another example of pure additive noise is random electromagnetic interference in a digital image detector.
An example of variable additive noise is photon shot noise associated with the Poisson statistics of photon counting in modern detectors, which varies as the square root of total photon count. Another example is film grain, which affects conventional photographic images and movies in a complex, but predictable, manner that depends on the photographic process and the local image value.
Pure and variable additive noise can significantly limit both the dynamic range and resolution of an image. Some examples, without implied limitation, include: low-light photography and cinematography of all sorts; medical imaging including magnetic resonance imaging, X-ray imaging or fluoroscopy, and computed-tomography scans; and astrophotography and astrophysical imaging.
Various techniques exist to reduce noise both in still images and in image sequences. For image sequences, such as video, conventional denoising methods use Fourier transforms, and also use a motion estimation process that estimates the degree of motion in portions of the sequenced images. The motion estimation process co-aligns features that are present in adjacent frames of the sequence, and makes use of temporal redundancy. However, the motion estimation process is ill-posed and imposes known difficulties. It also limits the use of the noise reduction technique on tomographic data or other non-temporal data sets that may be represented as a sequence of images.
Conventional denoising methods for image sequences sometimes refer to “3-D denoising”. However, this may mean 2-D transforms followed by 1-D transforms, and these methods include the above-described motion estimation. This approach is described in U.S. Pat. No. 8,619,881, and other references.